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Electromagnetic proton–neutron mass difference

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Abstract

We discuss the Cottingham formula and evaluate the proton–neutron electromagnetic mass difference exploiting the state-of-the-art phenomenological input. We decompose individual contributions to the mass splitting into Born, inelastic and subtraction terms. We evaluate the subtraction-function contribution connecting the input based on experimental data with the operator product expansion matched to QCD which allows us to avoid model dependence and to reduce errors of this contribution. We evaluate inelastic and Born terms accounting for modern low-\(Q^2\) data.

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Notes

  1. Without inputs from Ref. [32], the subtraction term contributes \(\delta M^{\mathrm {subt}}_{p-n} = 0.54 \pm 0.46~\mathrm {MeV}\).

  2. The proton and neutron mass corrections based on the state-of-the-art fits from Ref. [46] are in agreement with our results and have smaller uncertainties.

  3. A naive assignment of 3–5% error to nucleon structure functions gives an uncertainty estimate comparable to the inelastic contribution. A proper error estimate calls for reanalysis of nucleon structure functions taking correlations into account.

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Acknowledgements

We acknowledge Vadim Lensky and Marc Vanderhaeghen for useful discussion. This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG) through Collaborative Research Center “The Low-Energy Frontier of the Standard Model” (SFB 1044), in part by a NIST precision measurement grant and by the U. S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0019095, and in part by the Visiting Scholars Award Program of the Universities Research Association.

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  1. Institut für Kernphysik and PRISMA Cluster of Excellence, Johannes Gutenberg Universität, Mainz, Germany

    Oleksandr Tomalak

  2. Department of Physics and Astronomy, University of Kentucky, Lexington, KY, 40506, USA

    Oleksandr Tomalak

  3. Fermilab, Batavia, IL, 60510, USA

    Oleksandr Tomalak

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Correspondence to Oleksandr Tomalak.

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Tomalak, O. Electromagnetic proton–neutron mass difference. Eur. Phys. J. Plus 135, 411 (2020). https://doi.org/10.1140/epjp/s13360-020-00413-9

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